Classification based on fast and robust approximations to order statistics

A test system with four cameras in the infrared and visual spectra is under development at FFI (The Norwegian Defence Research Establishment). The system may be mounted on a jet aircraft or may be used in a land-based version. It can be used for image acquisition or for testing of automatic target recognition (ATR) algorithms. The sensors on board generate large amounts of data, and the scene may be rather cluttered or include anomalies (e.g. sun glare). This means we need algorithms which are robust, fast, able to handle complex scenes, and data from up to four sensors simultaneously. Typically, estimates of mean and covariance are needed for the processing. However, the common maximum likelihood (ML) estimates are in general too sensitive towards outliers. Algorithms based on order statistics are known to be robust and reliable. However, they are computationally very heavy. But approximations to order statistics do exist. Median of medians is one example. This is a technique where an approximation of the median of a sequence is found by first dividing the sequence in subsequences, and then calculating median (of medians) recursively. This technique can be applied for estimating the mean as well as the standard deviation. In this paper we extend this method for estimating the covariance matrix and the mean vector, and discuss the strategy with respect to robustness and computational efficiency. Applications for use in image processing and pattern recognition are given.